10 champions rotate weekly that are free to play. If you go to your summoner profile, to the champions tab, and check the box labeled "recommended", that will give you an idea of which champions to try out while you're still learning the ropes. After a few weeks of rotations, and several games under your belt, you'll get a good feel for what you like to play. Commonly, Ashe is the champion of choice for new players, as she is the tutorial champion, and she's a badass archer. But Ryze, Yi, and Nunu are pretty common as well.